A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m², what will be the cost of painting all these cones? (Use π= 3.14 and take √1.04 = 1.02 )
Answers & Comments
Sure, let's break it down:
1. Step 1: Calculate the slant height of the cone
The slant height (l) of a cone can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the slant height is the hypotenuse, the height (h) is one side, and the radius (r) is the other side. The formula is l = sqrt(h² + r²). Given that h = 1 m and r = 20 cm = 0.2 m, we can substitute these values into the formula. However, we are given that sqrt(1.04) = 1.02, so l = 1.02 m.
2. Step 2: Calculate the curved surface area of one cone
The formula for the curved surface area (CSA) of a cone is CSA = πrl. Substituting the given values, we get CSA = 3.14 * 0.2 m * 1.02 m = 0.64 m².
3. Step 3: Calculate the total surface area to be painted
Since there are 50 cones, the total surface area to be painted is 50 * CSA = 50 * 0.64 m² = 32 m².
4. Step 4: Calculate the total cost of painting
The cost of painting is Rs 12 per m². Therefore, the total cost of painting all the cones is 12 * total surface area = Rs 12 * 32 m² = Rs 384.
So, the cost of painting all these cones would be Rs 384.
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Answer:
Cost of painting the 50 hollow cones, if the cost of painting is Rs 12 m² is Rs 384.34
Step-by-step explanation:
Given that, a bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard.
Further given that, each cone has a base diameter of 40 cm and height 1 m.
So, we have
Height of cone, h = 1 m
Radius of cone, r = 20 cm = 0.2 m
We know, Slant height (l), height (h) and radius (r) is connected by a relationship
[tex] \sf \: {l}^{2} = {h}^{2} + {r}^{2} \\ [/tex]
[tex] \sf \: {l}^{2} = {(1)}^{2} + {(0.2)}^{2} \\ [/tex]
[tex] \sf \: {l}^{2} =1 + 0.04 \\ [/tex]
[tex] \sf \: {l}^{2} = 1.04 \\ [/tex]
[tex] \sf \: l = \sqrt{1.04} = \sqrt{ {(1.02)}^{2} } \\ [/tex]
[tex]\implies\sf\:l = 1.02 \: m \\ [/tex]
Thus, Slant height of a cone is 1.02 m
Now, Amount of paint required to to paint the 50 hollow cones is equals to 50 times the Curved Surface Area of cone.
Thus,
[tex] \sf \: Amount\:of\:paint\: required = 50\:\pi \: r \: l \\ [/tex]
[tex] \sf \: Amount\:of\:paint\: required = 50 \times 3.14 \times 0.2 \times 1.02\\ [/tex]
[tex] \implies\sf\: Amount\:of\:paint \: required = 32.028 \: {m}^{2} \\ [/tex]
Now, Further given that
[tex] \sf \: Cost\:of\: {1 \:m }^{2} \: of \: painting = Rs \: 12 \\ [/tex]
So,
[tex] \sf \: Cost\:of\:32.028 \: {m }^{2} \: of \:painting = 32.028 \times 12 \\ [/tex]
[tex]\implies\sf\: Cost\:of\:32.028 \: {m }^{2} \: of \: painting = Rs \: 384.34 \\ [/tex]
Hence, Cost of painting the 50 hollow cones, if the cost of painting is Rs 12 m² is Rs 384.34